A water storage tank is initially \frac{1}{3} full. When 28\text{ litres} of water are add… — JAMB UTME

A water storage tank is initially $\frac{1}{3}$ full. When $28\text{ litres}$ of water are added to the tank, it becomes $\frac{4}{5}$ full. What is the total capacity of the water tank?

A
$35\text{ litres}$
$60\text{ litres}$ Cevap
C
$84\text{ litres}$
D
$140\text{ litres}$

Cevap

The total capacity of the water tank is

60\text{ litres}

Subtracting the initial filled fraction (one-third) from the final filled fraction (four-fifths) yields seven-fifteenths. Since seven-fifteenths of the total capacity corresponds to 28 litres, dividing 28 by seven-fifteenths gives a total capacity of 60 litres.

Adım Adım Çözüm

Find the fraction of the tank filled by adding the

28\text{ litres}

of water.

Fraction added =

\frac{4}{5} - \frac{1}{3} = \frac{12 - 5}{15} = \frac{7}{15}

Subtracting the initial fraction filled from the final fraction filled gives the fractional change.

Set up an equation equating the fractional change to the actual volume added.

\frac{7}{15} \times C = 28

, where

C

represents the total capacity of the tank.

The fractional change multiplied by total capacity equals the physical volume of water introduced.

Solve for the total capacity

C

C = 28 \times \frac{15}{7} = 4 \times 15 = 60\text{ litres}

Multiplying both sides by the reciprocal of

\frac{7}{15}

yields the total capacity.

Anahtar Kavram

Fractional Word Problems and Quantity Determination

Tahmini Süre:1m 30s

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